Typically a DAC or ADC will require equal resistances for each resistor in a string. Other applications may require a string of resistors wherein the resistance values of the resistors are related, but not necessarily equal. For example, a string having uniform voltage per unit length can be implemented wherein the smallest possible resistance value equals n, and each of the resistors in the string can have a resistance value equal to a multiple of n. A resistor string according to the invention is especially suited for these applications.
DACs are used to convert a digitally coded signal to an analog signal, or in conjunction with successive approximation circuitry as part of an analog-to-digital converter. DACs convert a digitally coded signal to an analog signal, typically a voltage, that correspond, to the digitally coded signal. The analog signal can take on many different values over a predetermined range corresponding to the range of digitally coded signals.
DACs may employ a resistor string comprised of series coupled equal resistance resistors. Between contiguous resistors in the resistor string, as well as between the resistor string and an energy source energizing the resistor string, are intermediate taps. Switches, coupled between an output node and intermediate taps, when turned on, electrically couple the respective intermediate taps to the output node, and when turned off, isolate the intermediate taps from the output node.
The precision with which resistors are formed affects the precision of the resulting analog signal. A critical goal in the design of resistor strings is to reduce the amount of area required for the resistor string. Typically, the resistor string is the bulkiest part of the converter design from a silicon die area perspective. Direction reversals, or folding points, are typically employed to confine the resistor string to a limited area. Another goal is to be able to fabricate a resistor string demonstrating linearity, wherein, for example, each resistor has the same resistance. This goal is particularly elusive when folding points are incorporated into the string. Specifically, it is difficult to design a compact resistor string where the resistors near the folding points exhibit substantially identical resistance to resistors away from the folding points. Gross e, al., in U.S. Pat. No. 5,534,862, incorporated herein by reference, describe one approach to creating a resistor string with equal resistance resistors. However, the Gross et al. approach achieves linearity at the cost of devoting a large amount of area to the resistor string. It is preferable, and in fact mandated by design constraints of many modern applications, that a resistor string exhibit linearity while requiring less area than that required by the Gross et al. approach.